An advanced model for the description of fluid-solid mass transfer in packed beds is proposed, in which the effects of particle size distribution, grain swelling or shrinking and concentration dependence of diffusivity in the particle are taken into account. These effects are discussed regarding two situations encountered in chemical technology practice : extraction of low molecular compounds from polycaproamide and ion exchange recovery of aurocyanide ions from waste water of gold plating. Experimental data for these two processes are compared with model predictions. A very good coincidence is obtained in the case of extraction and qualitative agreement-in the case of ion exchange.